If tan 35=k then the value of tan145_ tan 125 by 1+tan 145 tan 125=
samyuktha64:
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Given, tan 35° = k
= (tan 145° - tan 125°)/(1+tan 145°.tan 125°)
= {tan (180-35) - tan (90+35)}/{1+tan (180-35).tan (90-35)}
= {-tan 35° - (-cot 35°)}/{1+(-tan 35°)(-cot 35°)
= {-k-(-1/k)}/{1+(-k)(-1/k)}
= (-k²+1/k) ÷ (1+1)
= -k²+1/2k
= (1-k²)/2k
= (tan 145° - tan 125°)/(1+tan 145°.tan 125°)
= {tan (180-35) - tan (90+35)}/{1+tan (180-35).tan (90-35)}
= {-tan 35° - (-cot 35°)}/{1+(-tan 35°)(-cot 35°)
= {-k-(-1/k)}/{1+(-k)(-1/k)}
= (-k²+1/k) ÷ (1+1)
= -k²+1/2k
= (1-k²)/2k
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